Materials for use in optical and optoelectronic applications

ABSTRACT

A single crystal ceramic material for optical and optoelectronic applications is d, including a single crystal spinel having a general formula aAD·bE 2 D 3 , wherein A is selected from the group consisting of Mg, Ca, Zn, Mn, Ba, Sr, Cd, Fe, and combinations thereof, E is selected from the group consisting Al, In, Cr, Sc, Lu, Fe, and combinations thereof, and D is selected from the group consisting O, S, Se, and combinations thereof. A ratio b:a&gt;1:1 such that the spinel is rich in E 2 D 3 , and the single crystal spinel is formed by a melt process

CROSS-REFERENCE TO RELATED APPLICATION(S)

[0001] This application is a continuation-in-part of application Ser.No. 09/863,013, filed May 22, 2001, published as US 2003/0007520 on Jan.9, 2003, priority to which is claimed.

BACKGROUND

[0002] 1. Field of the Invention

[0003] The present invention is generally directed to materials for usein optical and optoelectronic applications, and particularly materialsand processes for forming same having crystallographic structuresrelated to the spinet crystal structure.

[0004] 2. Description of the Related Art

[0005] Single crystal materials, such as those having or related to thespinet crystal structure have been used in various optical andoptoelectronic applications. For example, single crystal spinet bouleshave been formed and processed into wafers for fabrication ofoptoelectronic devices such as LEDs and lasers. In this context, wafersare sliced from a single crystal boule, then subjected to waferprocessing to form a plurality of devices in the form of individual die,which are then severed from the wafer. In other applications,spinel-based materials are formed into Q-switches for lasing operations.

[0006] Q-switching is a method for obtaining single laser pulses of veryhigh power by protracting the period of population inversion ofelectrons in excited states just prior to emission. Extending the periodof population inversions typically can be achieved acousto- orelectro-optically by use of shutters, mechanically (with an orthogonalmirror or rotating mirror), or by use of saturable absorbers (in theform of dyes or doped crystals).

[0007] The term “Q-switching” is a reference to the fact that a“Q-factor” or “Quality factor,” which can be defined as v/Δv_(c), wherev is cavity resonance frequency, and Δv_(c) is cavity linewidth, shiftsfrom a very low value to a very high value during laser pulse emission.More specifically, population inversion of electrons is extended byblocking emission from the laser cavity. At the time a laser pulse is tobe emitted, the blockage is removed, thereby causing the threshold gainof electrons to be deliberately and suddenly reduced. Populationinversion is much higher than the threshold gain value, and actual gaingreatly exceeds cavity losses. As a result, the excited states arequickly depopulated, causing energy to be discharged in a single laserpulse. The sudden discharge causes actual gain to be reduced to a pointbelow the threshold value, thereby terminating the pulse.

[0008] Saturable absorber Q-switches operate passively, wherebyabsorptivity of the laser wavelength decreases with increasingirradiance until “bleaching” occurs. Population inversion increasesuntil the Q-switch is bleached, at which time the threshold value isreduced, resulting in a laser pulse. Passive Q-switches typically areeasy to implement relative to other mechanisms. Historically, examplesof saturable absorber Q-switches are dyes, such as bis 4-dimethylarninodithiobenzyl-nickel (BDN) dissolved in 1,2 dichloroethane forNd:YAG lasers, and gases, such as SF₆ for CO₂ lasers.

[0009] More recently, solid state Q-switches have been employed thatinclude crystals doped with tetrahedrally coordinated Co²⁺ ions as atunable laser source in wavelengths that range from about 1.5 to about2.3 μm. Among the crystals that have been doped with Co²⁺ ions for 1.34μm Nd³⁺:YAlO₃ and 1.54 μm-Er³⁺:glass lasers are Y₃Al₅O₁₂, Y₃Sc₂Ga₃O₁₂,LaMgAl₁₁O₁₉, MgAl₂O₄ (MALO) and ZnSe. MgAl₂O₄ crystals, having thespinel crystal structure, include tetrahedral and octahedral positions.Co²⁺ dopant ions displace Mg²⁺ ions from tetrahedral positions of thecrystal. The amount of Co²⁺ ion dopant in MgAl₂O₄ crystals typicallyranges from about 0.0003 atomic weight percent to about 0.05 atomicweight percent. However, the frequency of the peak emission of dopedsolid state passive Q-switches typically is not affected by the amountof dopant. Further, the efficiency of a Q-switch (and, thus, the powerof the laser pulse) is significantly diminished if it does not have anabsorption band that matches the lasing transition. For example, spinelhaving the empirical formula of MgAl₂O₄ and doped with Co²⁺ typicallyhas an absorption band (⁴T₁ spectrum) of about 1536 nanometers (nm),whereas the lasing transition of Er:Yb:glass lasers is about 1540 nm.Generally, the efficiency of cobalt-doped spinel Q-switches inEr:Yb:glass and other lasers is limited by the difference in specificabsorption bands from the lasing transition wavelengths of such lasers.

[0010] Therefore, a need exists to significantly diminish or eliminatethe above-mentioned problems of cobalt-doped saturable absorberQ-switches.

SUMMARY OF THE INVENTION

[0011] According to one aspect of the present invention, a singlecrystal ceramic material for optical and optoelectronic applications isprovided. The material comprises a single crystal spinel having ageneral formula aAD·bE₂D₃, wherein A is selected from the groupconsisting of Mg, Ca, Zn, Mn, Ba, Sr, Cd, Fe, and combinations thereof,E is selected from the group consisting Al, In, Cr, Sc, Lu, Fe, andcombinations thereof, and D is selected from the group consisting O, S,Se, and combinations thereof, wherein a ratio b:a>1:1 such that thespinel is rich in E₂D₃, and the single crystal spinel is formed by amelt process.

[0012] According to another aspect of the present invention, a method offorming a monocrystalline spinel material includes: forming a melt, andgrowing a spinel single crystal from the melt. The single crystal spinelhas a general formula aAD·bE₂D₃, wherein A is selected from the groupconsisting of Mg, Ca, Zn, Mn, Ba, Sr, Cd, Fe, and combinations thereof,E is selected from the group consisting Al, In, Cr, Sc, Lu, Fe, andcombinations thereof, and D is selected from the group consisting O, S,Se, and combinations thereof, wherein a ratio b:a>1:1 such that thespinel single crystal is rich in E₂D₃.

[0013] Other embodiments are directed to a cobalt-doped saturableabsorber Q-switch, to a laser system that employs a cobalt-dopedsaturable absorber Q-switch, and to a method of forming a cobalt-dopedsaturable absorber Q-switch.

[0014] In one embodiment, the saturable absorber Q-switch includes amonocrystalline lattice having the formula Mg_(1-x)Co_(x)Al_(y) O_(z)where x is greater than 0 and less than 1, y is greater than 2 and lessthan about 8, and z is between about 4 and about 13. The lattice hastetrahedral and octahedral positions, and most of the cobalt andmagnesium occupies tetrahedral positions. In a preferred embodiment,essentially all of the cobalt and magnesium occupies tetrahedralpositions of the monocrystalline lattice.

[0015] In a laser system of the invention, a laser resonator cavity hasa resonant axis and a lasing element within the resonator cavity.Suitable means optically pump the lasing element. A saturable absorberQ-switch lies along the resonant axis of the laser resonator cavity. TheQ-switch includes a monocrystalline lattice having a formulaMg_(1-x)Co_(x)Al_(y)O_(z) where x is greater than 0 and less than about1, y is greater than 2 and less than about 8, and z is between about 4and about 13. The monocrystalline lattice has tetrahedral and octahedralpositions, and most of the magnesium and cobalt occupy tetrahedralpositions. In a preferred embodiment, essentially all of the magnesiumand cobalt occupy tetrahedral position of the monocrystalline lattice.In one embodiment, the lasing element is an Er:Yb:glass laser (or anylaser source of 1.5-1.6μ frequency). In another embodiment, the laserelement is a Nd³⁺:YAlO₃ lasing element.

[0016] A method of forming a monocrystalline lattice of a saturableabsorber Q-switch of the invention includes forming a melt of magnesium,cobalt, aluminum and oxygen, wherein the molar ratio ofmagnesium:cobalt:aluminum is (1-x):x:y, where x is greater than 0 andless than about 1, and y is greater than 2 and less than 8. A spinelseed crystal is immersed in the melt and rotated at a rate in a range ofbetween about 4 and about 12 revolutions per minute, while withdrawingthe seed crystal from the melt at a rate in a range of between about0.04″/hr and about 0.1″/hr to thereby form the monocrystalline lattice.In one embodiment, the melt is formed by combining MgO, Co₃O₄ and Al₂O₃powders, and then heating the combined powders to a temperaturesufficient to form the melt.

[0017] Embodiments of the present invention have several advantages. Forexample, the saturable absorber Q-switch of the invention includes aratio of aluminum to magnesium that is greater than that ofstoichiometric spinel (MgAl₂O₄) having an equal amount of cobalt dopant.Despite the relatively high ratio of aluminum to magnesium, most oressentially all magnesium and cobalt dopant occupy only tetrahedralpositions of the crystal. Modification of the relative amount ofaluminum to magnesium in the saturable absorber Q-switches of theinvention enables adjustment of the ⁴T₁ spectrum of cobalt dopant tomore closely match a peak of 1544 nanometers, which is the lasingwavelength of erbium:ytterbium:glass (Er:Yb:glass) lasers. In anotherembodiment, modification of the relative amount of aluminum to magnesiumalso enables emission of a band at about 1340 nanometers, which is aboutthe lasing wavelength of Nd³⁺:YAlO₃ lasers. Both emission bands cansignificantly increase the efficiency of saturable absorber Q-switchesemployed with such lasers. Also, the saturable absorber Q-switches ofthe invention generally are relatively stable at reduced temperatures,such as at about 8 Kelvin (K).

BRIEF DESCRIPTION OF THE DRAWINGS

[0018]FIG. 1 is a schematic representation of one embodiment of thelaser system of the invention, employing a cobalt-doped Q-switch of theinvention.

[0019]FIG. 2 shows light absorption in a 1:3 spinel as a function ofwavelength at 8 Kelvin (K).

[0020]FIG. 3 shows light absorption in a 1:3 spinel as a function ofwavelength at 300 Kelvin (K).

[0021]FIG. 4 shows fluorescence intensity of a 1:3 spinel as a functionof wavelength at 8 Kelvin (K).

[0022]FIG. 5 shows fluorescence intensity of a 1:3 spinel as a functionof wavelength at 300 Kelvin (K).

[0023]FIG. 6 is an overlay of FIGS. 4 and 5, as a comparison.

DETAILED DESCRIPTION OF THE INVENTION

[0024] The features and other details of the invention will now be moreparticularly described with reference to the accompanying figures andpointed out in the claims. It will be understood that the particularembodiments of the invention are shown by way of illustration and not aslimitations of the invention. The principal features of this inventioncan be employed in various embodiments without departing from the scopeof the invention. This application is related to and incorporates byreference the subject matter of copending application Ser. No. ______,filed Sep. 22, 2003, to Kokta et al., bearing attorney docket number1035-BI4282. This application is related to and incorporates byreference the subject matter for copending application Ser. No. ______,filed Sep. 22, 2003, to Kokta et al., bearing attorney docket number1035-BI4307. This application is also related to and incorporates byreference the subject matter for copending application Ser. No. ______,filed Sep. 22, 2003, to Stone-Sundberg et al., bearing attorney docketnumber 1035-BI4281.

[0025] In one embodiment, a single crystal ceramic material for opticaland optoelectronic applications is provided. The material comprises asingle crystal spinel having a general formula aAD·bE₂D₃, wherein A isselected from the group consisting of Mg, Ca, Zn, Mn, Ba, Sr, Cd, Fe,and combinations thereof, E is selected from the group consisting Al,In, Cr, Sc, Lu, Fe, and combinations thereof, and D is selected from thegroup consisting O, S, Se, and combinations thereof, wherein a ratiob:a>1:1 such that the spinel is rich in E₂D₃. In certain embodiments,the spinel is rich in E₂D₃ such that the ratio b:a is not less thanabout 1.2:1, 1.5:1, or even 2.0:1. Particular working embodiments have ab:a ratio of about 2:1 and 3:1. Typically, b:a does not exceed about4:1. Due in part to use of E₂D₃-rich compositions, the material haslower mechanical stress and/or strain as compared to stoichiometricspinels having a b:a ratio of 1:1.

[0026] In a particular embodiment, A is Mg, D is O, and E is Al, suchthat the single crystal spinel has the formula aMgO.bAl₂O₃. The materialmay consist essentially of a single phase of spinel, with substantiallyno secondary crystalline phases.

[0027] Generally, the single crystal spinel is formed by a melt process,by growing a boule from a melt provided in a crucible. Here, a seedcrystal, such as stoichiometric MgO.Al₂O₃ spinel is contacted to themelt provided in the crucible, the melt and the seed crystal are rotatedwith respect to each other, such as at a rate between 2 and 12 rpms, andthe seed crystal (with growing single crystal boule) are drawn from themelt.

[0028] In another embodiment, the material further includes Co,providing a saturable absorber Q-switch. The Q-switch has amonocrystalline lattice, wherein the monocrystalline lattice has aformula of Mg_(1-x)Co_(x)Al_(y)O_(z), and wherein x is greater than 0and less than about 1, y is greater than 2 and less than about 8, and zis between about 4 and about 13. The monocrystalline lattice of thesaturable absorber Q-switch employed in the laser system of theinvention has tetrahedral and octahedral positions, and most of themagnesium and cobalt occupy tetrahedral positions. Preferably,essentially all of the cobalt and magnesium occupy tetrahedralpositions.

[0029] An example of a laser system of the invention is shown in FIG. 1.As shown therein, laser system 10 includes resonator cavity 12.Resonator cavity 12 is defined by flat mirror 14 and outcoupler mirror16. Flat mirror 14 and outcoupler mirror 16 are oriented along aresonant axis 18, whereby a light beam within resonator cavity 12 canoperate in a cavity mode. Lasing element 20 is located along resonantaxis 18 within resonator cavity 12. Typically, lasing element 20 is acylindrical rod oriented parallel to resonant axis 18. Examples ofsuitable lasing elements include Er:Yb:glass (erbium:ytterbium:glass),Er:glass (erbium doped into a phosphate glass host) and Nd³⁺:YAlO₃(erbium doped into a yttrium-aluminum oxide host).

[0030] A suitable means for optically pumping the lasing element,optical pump 22, is proximate to lasing element. Focusing lens 24 islocated between lasing element 20 and outcoupler mirror 16.

[0031] Q-switch 26 is located between focusing lens 24 and outcouplermirror 16. Saturable absorber Q-switches of the invention include amonocrystalline lattice of a cobalt-doped spinel-like material whereinthe molar ratio of aluminum to the sum of magnesium and cobaltcomponents of the monocrystalline lattice exceeds 2:1. Morespecifically, the saturable absorber Q-switch of the invention includesa monocrystalline lattice having the formula Mg_(1-x)Co_(x)Al_(y)O_(z)where x is less than 1 (in some embodiments greater than 0), y isgreater than 2 and less than 8, and z is between about 4 and 13. A “1:1spinel” refers to an embodiment wherein y is about 2. A “1:2 spinel”refers to an embodiment where y is about 4. A “1:3 spinel” refers to anembodiment where y is about 6. Most of the magnesium and cobalt of thesaturable absorber Q-switch occupy tetrahedral positions of themonocrystalline lattice. In a preferred embodiment, essentially all ofthe cobalt and magnesium occupy tetrahedral positions.

[0032] In one embodiment of the invention, the monocrystalline latticehas a value of z of about 4. In another embodiment, y is about 4 and zis about 7. In still another embodiment, y is about 6 and z is about 10.Generally, the saturable absorber Q-switch has a ⁴T₁ spectrum betweenabout 1537 nm and about 1544 nm. In one preferred embodiment, whereinthe lasing element of the laser system of the invention is an Er:Yb:glass lasing element, the value of y is sufficient to cause themonocrystalline lattice of the saturable absorber Q-switch to have a ⁴T₁spectrum of cobalt ion (Co²⁺) to emit light at a wavelength of at leastabout 1.54 μm (1540 nm). In an especially preferred embodiment, thesaturable absorber Q-switch has an absorption band of about 1544 nm.

[0033] In another preferred embodiment, such as wherein the lasingelement is a Nd³⁺:YAlO₃ lasing element, the value of y is sufficient tocause the monocrystalline lattice to have an absorption band of betweenabout 1337 nm and about 1365 nm, such as an absorption band of 1337 nm,1360 nm, 1365 nm or, most preferably, about 1340 nm.

[0034] In one embodiment, the excited state absorption for the cobaltion in the saturable absorber Q-switch of the invention is about thesame as that of a saturable Q-switch absorber wherein a molar ratio ofaluminum to the combined magnesium and cobalt amount is about 2.Generally, the unit cell dimension of the monocrystalline lattice willbe less than about 8.085 Å. In a preferred embodiment, the unit celldimension is between about 7.970 Å and about 8.083 Å. In still anotherembodiment, the saturable absorber Q-switch of the invention has a decaytime (τ₃₁) greater than about 30×10⁻⁶ seconds.

[0035] Typically, the amount of cobalt ion in the saturable absorberQ-switch of the invention is greater than about 0.02 atomic percent.Preferably, the amount of cobalt ion present is in an amount in a rangeof between about 0.02 and about 0.043 atomic percent of themonocrystalline lattice.

[0036] The saturable absorber Q-switches of the invention can be formedby use of a spinel seed (MgAl₂O₄) having a major axis oriented along the<111> axis. Preferably, the spinel seed is cylindrical. The crystal isgrown, for example, in an inductively-heated ten kHz radiofrequency (RF)generator. Control of crystal growth can be maintained by use ofsuitable computer software, such as Automatic Diameter Control (ADC)software, commercially available from, for example, FEC Crystal GrowingSystems, which can control the shape of the growing crystal, temperatureincrease, cooling rates, and other pertinent parameters. Crystal growthis commenced by heating a growth chamber of a suitable crucible, such asan iridium crucible, containing thoroughly mixed powders of magnesiumoxide (MgO), cobalt oxide (Co₃O₄) and aluminum oxide (Al₂O₃). The growthchamber is heated to a suitable temperature, such as a temperature in arange of between about 1900° C. and about 2150° C. Preferably, thegrowth chamber is heated to a temperature of about 2150° C. to form amelt.

[0037] The spinel seed is immersed into the molten mixture and rotatedwhile being withdrawn from the growth medium at a controlled rate. Inone embodiment, the withdrawal rate is in a range of between about 0.25and about 1.0 millimeters per hour at a rotation speed in a range ofbetween about 4 and about 12 revolutions per minute (RPM). Preferably,the withdrawal rate is about 1 millimeter per hour and the rotation ofthe seed is about 8 RPMs. Crystal growth continues for a suitable periodof time to form a monocrystalline lattice of suitable dimension. In oneembodiment, crystal growth is continued for a period of about 150 hours.Thereafter, the crystal is cooled to about 25° C. over a period of timein a range of between about 72 and about 100 hours. Preferably, thecrystal is cooled from the melt temperature, of about 2150° C. to about25° C. over a period of time of about 100 hours. Thereafter, the crystalcan be machined by known methods to form the saturable absorber Q-switchof the invention.

[0038] The invention is illustrated by the following examples, which arenot intended to be limiting in any way.

EXEMPLIFICATION EXAMPLE 1 General Method for Spinel Growth

[0039] The various cobalt doped spinel compositions were grown on 1:1(MgAl₂O₄) spinel seed oriented along the <111> axis. Desiredcompositions were melted in iridium crucibles of sizes appropriate forgrowth of 30 mm diameter, and 50 mm diameter crystals. The sizes of themelts for larger crystals were circa 3000 gms. The iridium crucibleswere inductively heated by 10 kHz RF (radio-frequency) generators. Thediameter control was based on controlling the growing crystals weightvia controlling the generator output in accordance to the signal from aload cell. On an average, the melting point of the spinel was about 100degrees higher than the melting point of sapphire. Prior to and duringthe growth, the melts were maintained under an ambient atmospherestrictly inert. The volatility of the Co oxide dopant was very low. TheCo oxide apparently reacted with the spinel components on the heat up,and did not evaporate from the melt. The crystals of 1:1 and 1:2compositions appeared to grow relatively easily, with linear growthrates exceeding 1-2 mm/hr. The charge preparation in a case of the 1:3compound included a very thorough mixing of the constituent oxides. Inaddition, the results were sensitive to establishing a good equilibriumcondition during seeding of the crystal, and also to the crystal growthrate.

EXAMPLE 1A 1:3 Spinel Growth

[0040] Composition

[0041] 206.05 gms of MgO

[0042] 0.41 gms of Co₃O₄

[0043] 1043.54 gms of Al₂O₃

[0044] The composition was mixed and loaded into 3″ diameter 4½″ talliridium crucible of 440 ml volume. The crucible was placed into growthsystem comprising RF (radio frequency), generator (power) supply, agrowth chamber containing the RF coupling coil, zirconium oxideinsulation material in an ambient gas enclosure—“Bell Jar,” and anelectronic control system. Control was accomplished by controlling theRF generator output in response to the mass of the growing crystal.“ADC” (Automatic Diameter Control) software, supplied by F. Bruni,controlled the shape of growing crystal, temperature increase, and cooldown rates, and all other pertinent parameters. The crucible with theoxide mixture was heated to 2150° C. to form a melt. <111> spinel “seed”(small rod-shaped crystal) was immersed (dipped) into the moltenmixture. Applying a withdrawal rate of 1 mm/hr along with rotation ofthe seed at 8 rpm, the crystal growth was started. Growth continued for150 hours followed by a 100 hour cool down period.

[0045] Result: A blue crystal, “Spinel” crystal structure, ¼″ diameter,7″ long A₀=8.012A⁰ Optical measurement: O.D. (Optical Density): 0.7 cm⁻¹

EXAMPLE 1B 1:2 Spinel Growth

[0046] Composition

[0047] 141.56 gms of MgO

[0048] 0.87 gms of Co₃O₄

[0049] 1107 gms of Al₂O₃

[0050] The composition was loaded into same crucible as described inExample #1, and placed in an identical growth system. Heat-up time was 6hours to 2150° C. Rotation rate applied was 8 rpm, pull rate 1 mm/hrunder strictly inert atmosphere. Growth time of 150 hours was followedby a 100 hour cool-down period. Grown crystal was harvested at roomtemperature.

[0051] Result: A blue crystal

[0052] Structure: “Spinel”

[0053]_(A0)=7.97 A⁰

[0054] Optical Density: 2.4 cm⁻¹

EXAMPLE 1C 1:1 Spinel Growth

[0055] Composition

[0056] 353.68 gms of MgO

[0057] 0.70 gms of CO₂O₃

[0058] 895.62 gms of Al₂O₃

[0059] Raw materials were mixed and loaded into an iridium crucible. Thecrucible was placed in the previously described system. Temperature wasincreased over a period of 6 hours to 2150° C. to complete melting.<111> spinel seed was immersed (dipped) into the melt. A withdrawal rateof 1 mm/hr, crystal growth was started. Growth continued for 150 hoursfollowed by a 100 hour cool down period.

[0060] Result: A single crystal spinel ¼″ diameter, 7″ long

[0061] Structure: “Spinel”

[0062] Optical Density: 0.63 cm⁻¹

EXAMPLE 2 Experimental Details

[0063] Crystals of MgAl₂O₄, MgAl₄O₇, and MgAl₆O₁₀ doped with varyingamounts of cobalt from 0.02 to 0.04 percent atomic cobalt were grown bythe method described in Example 1. We labeled the different spinelsaccording to 1:1 (MgO.Al₂O₃), 1:2 (MgO.2Al₂O₃), and 1:3 (MgO.3Al₂O₃).The structural analysis for each crystal gave unit cell dimensions of8.083 Å for 1:1, 8.012 Å for 1:2, and 7.970 Å for 1:3. Each spinelbelonged to the space group O_(h) ⁷-Fd3m with the Mg²⁺ ions havingtetrahedral coordination with full T_(d) symmetry and the Al³⁺ ionshaving octahedral coordination (P. R. Staszak, et al., J. Phys C: SolidState Phys., 17:4751 (1984) and H. St. C. O'Neill and A. Navrotsky, Am.Mineralogist, 68:181 (1983), the teachings of which are incorporatedherein by reference in their entirety). The lattice constant for 1:1reported in the literature was 8.085 Å (R. D. Gillen and R. E. Salomon,J. Phys. Chem., 74:4252 (1970), the teachings of which are incorporatedherein by reference in their entirety). Previous studies, includingthermodynamic phase diagram analyses of MgO.nAl₂O₃ and optical studiesof Co²⁺, showed a strong preference for Co²⁺ in tetrahedral sites whenthe crystal had both tetrahedral and octahedral cation sites (A.Navrotsky and O. J. Kleppa, J. Inorg. Nucl. Chem., 29:2701 (1967); A.Navrotsky and O. J. Kleppa, J. Inorg. Nucl. Chem., 30:479 (1968); A.Navrotsky, et al., J. Am. Ceramic Soc., 69:418 (1986); A. Navrotsky, Am.Mineralogist, 79:589 (1994); and N. V. Kuleshov, et al., J.Luminescence, 55:265 (1993), the teachings of which are incorporatedherein by reference in their entirety). Our results, described infra,indicated that the tetrahedral site were preferred sites of occupationby Co²⁺.

[0064] Polished samples used in spectroscopic measurements ranged fromcircular disks 4 cm in diameter and 0.5 cm thick, to rectangular piecesfor low-temperature studies that measured 10 mm by 5 mm by 2.15 mmthick. Crystals having the optimum optical density at 1.54 μm wereexamined for use as saturable absorbers. Room temperature absorptionspectra were obtained between 3000 nm and 300 nm with a Perkin-ElmerLambda-nine spectrophotometer. Calibration of the instrument over thewavelength of interest indicated that spectral lines and bands weremeasured to an accuracy of 0.22 nm. The low temperature (8K) absorptionspectrum was obtained with an upgraded Cary Model 14R spectrophotometercontrolled by a desktop computer. The spectral bandwidth was set at 0.5nm and the instrument was internally calibrated to an accuracy of 0.3nm. Spectra were analyzed and plotted by using the computer softwareprogram Sigma Plot. Fluorescence spectra at room temperature and at 8Kwere also obtained by using the instrument together with appropriatemirrors and filters and a Spex Model 340 E monochromator. Forfluorescence studies, excitation at 514.5 nm was provided by an argonion laser.

[0065] For low-temperature studies, the sample was mounted at the coldfinger of a CTI Model-22 closed-cycle helium cryogenic refrigeratorcapable of operation between 8K and room temperature. The sampletemperature was monitored with a silicon-diode sensor attached to thebase of the sample holder and maintained by using a Lake Shore controlunit.

[0066] The fluorescence lifetime of the strongest emission band centeredbetween 650 nm and 700 nm was measured by exciting each sample with thesecond harmonic (532 nm) of a Quanta-Ray pulsed Nd:YAG laser ModelGCR-12S. The pulse width was about 6 ns and the beam divergence was lessthan 0.5 μrad. The output energy was 15 mJ at 10 Hz. The signal wasdetected by a photomultiplier tube attached to the exit slit of themonochromator and sent to a 150 MHZ Tektronix oscilloscope Model 2445Ahaving a resolution of 10 ns.

[0067] Observed Spectra

[0068] The room temperature absorption spectrum of Co²⁺ in the threespinel crystals is given in Table 1. The concentration of Co²⁺ in eachsample was 0.033% (atomic weight percent, or “at.”) Co for 1:1, 0.02%at. Co for 1:2, and 0.0429% at. Co for 1:3. The general features in allthree spectra were similar and consisted of two relatively strong bandscentered near 600 nm and 1350 nm and weaker bands appearing between 550nm and 470 nm, and between 2500 nm and 1900 mn (N. V. Kuleshov, et al.,J. Luminescence, 55:265 (1993), the teachings of which are incorporatedherein by reference in their entirety). However, comparable peaks andbands showed a noticeable shift to longer wavelengths from the 1:1crystals to the 1:3 crystals. Of particular interest was the shift ofthe ⁴T₁ spectrum of Co²⁺ in the 1:3 sample to wavelengths even morefavorable for Q-switching at 1.54 μm than the saturable absorberCo²⁺:MgAl₂O₄ (the 1:1 host crystal) (J. B. Gruber, et al., Proc. ofSPIE, 3928:142 (2000), the teachings of which are incorporated herein byreference in their entirety). The peak at 1544 nm was observed wherestimulated emission occurred in the Er:Yb:glass laser. Its estimatedabsorption cross section at this wavelength was higher than the valueemployed for Co²⁺:MgAl₂O₄ (4×10⁻¹⁹ cm²) and was considerably larger thanthe stimulated emission cross section of Qx/Er at 1535 nm (0.6×10⁻²⁰cm²) (V. P. Mikhailov, et al., OSA TOPS, 21(ASSL):145 (1999); M. B.Carmargo, et al., Opt. Letts, 20:339 (1995); J. B. Gruber, et al., Proc.of SPIE, 3928:142 (2000); and R. Wu, et al., OSA TOPS, 22(ASSL):421(2000), the teachings of which are incorporated herein by reference intheir entirety). Excited state absorption (ESA) for Co²⁺ near 1540 nm in1:1 samples has been reported by several groups (V. P. Mikhailov, etal., OSA TOPS, 21(ASSL):145 (1999); M. B. Carmargo, et al., Opt. Letts,20:339 (1995); and M. Birnbaum, et al. OSA TOPS, 19(ASSL):148 (1997))including our group (J. B. Gruber, et al., Proc. of SPIE, 3928:142(2000)) that has done extensive modeling studies on saturable absorbers.The ESA cross section for Co²⁺ in the 1:3 compound, was similar to thevalue reported by Co²⁺ in the 1:1 compound (M. B. Carmargo, et al, Opt.Letts, 20:339 (1995)).

[0069] The similarity in the room temperature spectra of the threesamples led us to examine the details of the absorption spectrum forCo²⁺:MgAl₄O₁₀ at 8K. Table II presents the absorption spectrum between2590 nm and 476.5 nm. FIGS. 2 and 3 show light absorption of the 1:3spinel as a function of wavelength at 8 Kelvin and 300 Kelvin,respectively. The pattern of light absorption between 1200 mm and 1600mm indicates possible use of this material for passive Q-switches for“eye-safe” (1.546μ (micron)) lasers, but also for lasers operating in arange of between about 1.3 and about 1.35μ, which is useful in medicineas well as in optical communications business. The comparison at the twotemperatures indicates that the material also is useful at roomtemperature. The observed spectra were similar to the spectra reportedearlier for Co²⁺ ions in tetrahedral sites in MgAl₂O₄ (N. V. Kuleshov,et al., J. Luminescence, 55:265 (1993), the teachings of which areincorporated herein by reference in their entirety). There were somedifferences in the magnitude of the crystal-field splitting of Co₂₊ intetrahedral sites which can be seen by comparing the energy levels inTable II., col. 5, with the energy levels of Co²⁺ in ZnAl₂O₄, for whichthe data of Ferguson, et al. (J. Ferguson, et al., J. Chem. Phys.,51:2904 (1969)) allowed us to do extensive modeling (J. B. Gruber, etal., Proc. of SPIE, 3928:142 (2000). Table II, Col. 2, shows theTanabe-Sugano labels where (^(2s+1)L) represents the principal state(either quartet or doublet); the wavelength, absorption coefficient andthe energy of the transition are given in Cols. 3-5. The energy-levelcalculations and modeling are described below.

[0070] The fluorescence spectra at 8K and at 300K were characterized bya strong emission band between 600 nm and 700 nm. As can be seen inFIGS. 4, 5 and 6, fluorescence emissions as a function of wavelength of1:3 spinels are comparable at 8 Kelvin and 300 Kelvin. These materialsare useful as active materials for broadly tunable lasers. Also, twovery weak, broad bands centered around 920 nm and 1300 nm whichtypically were observed only in more concentrated samples (N. V.Kuleshov, et al., J. Luminescence, 55:265 (1993)). The assignment of thetransitions could be made with help from the analysis of the levelsgiven in Table II. The strong red emission band centered at 660 nm wasdue to vibronic and electronic transitions from the ²E, ⁴T excitedstates to the ground state, ⁴A₂, the weak broad band observed at 920 nmrepresented similar transition types from ²E, ⁴T₁ to the ⁴T₂ state, andthe weak band around 1300 nm represented vibronic and electronictransitions from ²E, ⁴T₁ to the ⁴T₁ manifold observed in absorptionbetween 1540 nm to 1230 nm. A weak band observed at 725 nm at 8K mayhave represented ²A₁□⁴T₂ transitions (see FIG. 5).

[0071] The room temperature fluorescence of the Co²⁺(²E⁴T₁I) state was asingle exponential, and the lifetime was measured to be about 30 μs. Theemission intensity did not appear to change appreciably with decrease intemperature to 8K, and so we did not expect the low temperature lifetimeto vary significantly from the room temperature value. Using crystals ofthe 1:1 sample containing between ten and twenty times more Co²⁺ than wereport, in Table II, for Co²⁺:MgAl₄O₁₀. Kuleshov, et al. (. V. Kuleshov,et al., J. Luminescence, 55:265 (1993)), found that the luminescencelifetime for all three bands was the same. The emission decay wasstrongly nonexponential and dependent on the temperature and Co²⁺ ionconcentration. However, their results were expected given the extent towhich the 3d⁷ orbitals interacted with the lattice of the host crystalat such Co²⁺ ion concentrations.

[0072] Energy Levels of Co²⁺

[0073] The absorption spectra of Co²⁺ (3d⁷) in tetrahedral cation sitesof the spinels consist of vibronically-coupled electronic transitions(including zero-phonon transitions) from the ground state ⁴A₂(⁴F) toexcited quartet states such as ⁴T₂(⁴F) and ⁴T₁(⁴P), and excited doubletstates, including ²E(²G), ²T₁(²G), ²A₁(²G), ²T₁(²P), and ₂T₂(²H). Theelectronic (Stark) levels for the 3d⁷ configuration are determined usinga Hamiltonian that consists of atomic and crystal-field terms (C. A.Morrison, “Crystal Fields for Transition-Metal Ions in Laser HostMaterials,” (Springer, N.Y.) (1992), the teachings of which areincorporated herein by reference in their entirety). The atomic or“free-ion” part is given as, $\begin{matrix}{{{\hat{H}}_{Fl}^{(} = {{\sum\limits_{{k = 2},4}{F^{(K)}{\sum\limits_{i > j}^{n}{{C_{kq}^{n}\left( \hat{i} \right)}{C_{kq}\left( \hat{j} \right)}}}}} + {\alpha {\hat{L}\left( {\hat{L} + 1} \right)}} + {\gamma \quad {G\left( {\hat{R}}_{5} \right)}} + {\zeta_{d}{\sum\limits_{j}{{\overset{\_}{l}}_{\overset{\_}{l}} \cdot {\overset{\_}{s}}_{l}}}}}},} & (1)\end{matrix}$

[0074] where F^((k)) are the Slater coulombic repulsion parametersbetween equivalent d electrons, α and γ are interconfigurationparameters and ζ_(d) is the spin-orbit coupling parameter for the 3delectrons (C. A. Morrison, “Angular Momentum Theory Applied toInteractions in Solids,” (Springer, N.Y.) (1988), the teachings of whichare incorporated herein by reference in their entirety). Thecrystal-field terms for Co²⁺ in tetrahedral sites are given$\begin{matrix}{{{\hat{H}}_{CF} = {{B_{20}{\sum\limits_{i}{C_{20}\left( \hat{i} \right)}}} + {B_{40}{\sum\limits_{i}{C_{20}\left( \hat{i} \right)}}} + {B_{44}{\sum\limits_{i}\left\lbrack {{C_{44}\left( \hat{i} \right)} + {C_{4 - 4}\left( \hat{i} \right)}} \right\rbrack}}}},} & (2)\end{matrix}$

[0075] as,

[0076] where the B_(nm) represent crystal-field parameters that arerelated to the lattice-sum parameters, A_(nm), through thethree-parameter theory with B_(nm)=ρ_(n)A_(nm) (C. A. Morrison, et al.,Chem. Phys., 154:437 (1991), the teachings of which are incorporatedherein by reference in their entirety). The initial set of atomic andcrystal-field parameters are listed in Table III and are obtained fromseveral sources (C. A. Morrison, “Crystal Fields for Transition-MetalIons in Laser Host Materials,” (Springer, N.Y.) (1992). We treat F^((k))and the three B_(nm) parameters as adjustable, beginning with a set ofF⁽²⁾ and F⁽⁴⁾ proposed originally by Morrison (C. A. Morrison, “CrystalFields for Transition-Metal Ions in Laser Host Materials,” (Springer,N.Y.) (1992)) and an initial set of B_(nm) based on lattice-sum modelingusing ion separations based on our x-ray crystallography studies of thespinel series.

[0077] Matrix elements for the Hamiltonian were computed usingcoefficients of fractional parentage for the 3d⁷ electronicconfiguration. The complete Hamiltonian was diagonalized in the basisstates S,L, and the calculated levels for Co²⁺ in MgAl₆O₁₀ are given asan example in Table II, Col. 6. The splitting of the ground-state,⁴A₂(⁴F) was not fully resolved in the temperature-dependent spectra. Thepredicted splitting given in table II is 5 cm⁻¹. The observed splittingin Co²⁺:ZnAl₂O₄, wherein Co²⁺ occupies the Zn²⁺ tetrahedral site, was 12cm⁻¹ (J. Ferguson, et al., J. Chem. Phys., 51:2904 (1969), the teachingsof which are incorporated herein by reference in their entirety). Onlyone of the observed levels was used to establish the energy of the⁴T₂(⁴F) state since the spectra of this manifold were very weak in the0.0429% at Co spectrum reported in Table II. Longer pathlengths andgreater concentrations of Co²⁺ provided spectra that support thepredicted levels 3 through 8 for this manifold splitting. Levels 15through 25 showed a strong mixing of ²G states into the ⁴p states (Col.7, Table II). Many of the zero-phonon transitions allowed in T_(d)symmetry were obscured by the vibronic bands making it difficult toattempt an overall fitting of the observed-to-calculated energy levels.However, the continuity in general band shape and structure throughoutthe series was predicted very well, with the final set of spectroscopicparameters given in Table III. TABLE I Room temperature absorption bandsof Co²⁺ in MgO.nAl₂O₃ MgAl₂O₄ MgAl₄O₇ MgAl₆O₁₀ STATE^(α) Λ (nm)^(b)α^(c) (cm⁻¹) E (cm⁻¹)^(d) Λ (nm)^(b) α^(c) (cm⁻¹) E (cm⁻¹)^(d) Λ(nm)^(b) α^(c) (cm⁻¹) E (cm⁻¹)^(d) ⁴T₂ 2519 0.03 3970 2556 0.04 39122580 0.05 3870 2448 0.03 4085 2476 0.04 4039 2500 0.04 4000 (⁴F) 2365(sh) 0.05 4228 2390 (sh) 0.05 4184 2252 0.05 4441 2279 0.07 4388 23000.09 4347 2163 0.03 4623 2190 (sh) 0.05 4566 2220 (sh) 0.06 4505 ⁴T₁1536 5.21 6510 1537 5.78 6506 1544 5.91 6476 (⁴F) 1417 4.82 7057 14505.12 6897 1460 (sh) 5.32 6849 1350 5.03 7407 1360 5.32 7353 1365 5.507326 1229 4.36 8137 1234 4.72 8104 1238 4.50 8077 ²E (²G) 671 1.36 14900672 1.28 14880 675 1.31 14815 ⁴T₁ 625 16.3 16000 626 14.3 15974 628 15.615923 (⁴P) 598 15.9 16722 599 14.7 16694 598 15.2 16700 580 17.1 17241581 16.0 17211 583 17.2 17150 ²A₁ 545 2.8 18343 545 2.8 18348 546 2.618315 (²G) ²T₁ 475 0.8 21053 476 0.7 21008 476.5 0.8 20986 (²P)

[0078] TABLE II Absorption spectra of Co²⁺ in MgAl₄O₁₀ at 8 K^(a)MgAl₄O₁₀ E (cm⁻¹) Level State Λ (nm)_(abc) α (cm⁻¹) E (cm⁻¹) Calc.^(b)Mixture SL States^(c) 1 ⁴A₂ 0 −7 1.00 ⁴F 2 (⁴F) −2 1.00 ⁴F 3 ⁴T₂ 2590 vwk 3861 3728 0.98 ⁴F + 0.01 ⁴P + 0.01 ¹G 4 (⁴F) 2500  (b) vwk 4000 40190.99 ⁴F + 0.01 ²G 5 2400  (b) vwk 4166 4146 0.99 ⁴F + 0.01 ⁴P 6 44110.99 ⁴F + 0.01 ⁴P 7 2231.5^(d) 1.11 4481 4544 0.99 ⁴F + 0.01 ⁴P 8 2110 vwk 4739 4713 0.99 + ⁴F + 0.01 ⁴P 9 ⁴T₁ 1539^(d) 5.33 6498 6479 0.91⁴F + 0.09 ⁴P 10 (⁴F) 1460  (sh) 4.82 6849 6854 0.86 ⁴F + 0.13 ⁴P + 0.01²G 11 1337^(d) 5.24 7479 7507 0.99 ⁴F + 0.01 ⁴P 12 7925 0.95 ⁴F + 0.01⁴P + 0.01 ²D (2) 13 1241^(d) 4.17 8058 8065 0.91 ⁴F + 0.08 ⁴P + 0.01 ²D(2) 14 1230  (sh) 3.82 8130 8119 0.97 ⁴F + 0.02 ⁴P + 0.01 ²D (2) 15 ⁴E673^(d) 1.12 14860 14877 0.39 ²G + 0.20 ⁴P + 0.15 ²P 16 (²G) 670  (sh)1.00 14925 14913 0.56 ²G + 0.17 ⁴P + 0.15 ⁴F 17 ⁴T₁ Band 3.0 15267 152460.65 ⁴P + 0.18 ²G + 0.11 ⁴F 18 (⁴P) Band Unresolved 15356 0.45 ²G + 0.18²P + 0.15 ⁴P band 19 Band 15357 0.66 ²G + 0.13 ²D (2) + 0.09 ²H 20 Band15690 0.49 ²G + 0.20 ²P + 0.16 ²H 21 15718 0.48 ⁴P + 0.24 ²G + 0.14 ²P22 621^(d) 15.07 16103 16167 0.90 ⁴P + 0.06 ²G + 0.02 ⁴F 23 605^(d) 16.116529 16451 0.67 ⁴P + 0.22 ²G + 0.04 ²H 24 598  17.40 16722 16696 0.82⁴P + 0.11 ²G + 0.02 ²H 25 583  (b) 18.1 17150 16852 0.70 ⁴P + 0.23 ²G +0.04 ²H 26 ²A₁ 552  (sh) 11.0 18116 18080 0.65 ²G + 0.21 ⁴P + 0.07 ²D(1) 27 (²G) 546^(d) 9.3 18315 18286 0.85 ²G + 0.09 ²D (2) + 0.03 ²D (1)28 18389 0.87 ²G + 0.05 ²D (2) + 0.07 ²H 29 Band 18746 0.63 ²G + 0.24 ²D(2) + 0.08 ²D (1) 30 19831 0.42 ²G + 0.37 ²P + 0.12 ²H 31 500^(d) 0.720000 19870 0.43 ²G + 0.40 ²P + 0.09 ²H 32 ²T₁ 490  (sh) 0.50 2040820494 0.62 ²2P + 0.23 ²G + 0.08 ²H 33 (²P) 0.60 20986 20862 0.34 ²H +0.25 ²G + 0.23 ²D (2) 34 ²T₂ 21476 0.45 ²H + 0.24 ²D (2) + 0.18 ²G 35(²H) 21906 0.41 ²D (2) + 0.36 ²H + 0.10 ²D (1)

[0079] TABLE III Spectroscopic parameters for Co²⁺ in T_(d) sites^(a)MgAl₂O₄ MgAl₄O₇ MgAl₆O₁₀ Initial Final Initial Final Initial Final ValueValue Value Value Value Value Parameter (cm⁻¹)^(b) (cm⁻¹) (cm⁻¹)^(c)(cm⁻¹) (cm⁻¹)^(d) (cm⁻¹) F⁽²⁾ 59367 59746 60520 61050 61045 61542 F⁽⁴⁾42210 41946 41843 41325 41705 40168 B₂₀ 2720 2566 2641 2814 3119 3949B₄₀ −8640 −8693 −8714 −8920 −9267 −9081 B₄₄ 5163 5120 5092 5040 51715242 ζ_(d) 420 420 537 537 515 515 α 86 86 108 108 108 108

[0080] Modeling of Crystals as Saturable Absorbers

[0081] Co₂₊ has been modeled as a saturable absorber for passivelyQ-switching the eyesafe (1.54 μm) Er:Yb:glass laser (J. B. Gruber, etal., Proc. of SPIE, 3928:142 (2000)). The model makes use of the rateequations based on quasi-three level gain medium and a four-levelabsorber that includes excited-state absorption (ESA). The model wasexpanded to include energy transfer between Yb and Er and excited stateabsorption in the gain medium. The spectroscopic parameters for thevarious gain media are available in the open literature (J. B. Gruber,et al., Proc. of SPIE, 3928:142 (2000), the teachings of which areincorporated herein by reference in their entirety)). For the saturableabsorber Co²⁺:MgAl₆O₁₀, which we modeled recently, we usedconcentrations equivalent to that reported in the present study; anindex of refraction we determined near 1.54 μm (1.742); an experimentalσ(gs)=5.2×10⁻¹⁹ cm²; an experimental σ(gs)=1.87×10⁻¹⁹ cm², and a delaytime (τ₃₁) of 30×10⁻⁶s.

[0082] The 1:3 material is a better performer as a saturable absorberthan 1:1 and 1:2 spinels given comparable Co₂₊ ion concentrations and alaser cavity design that is the same for all three spinel samples.

[0083] In summary, all members of the series may prove to be efficienthigh performance absorbers for Q-switching at the 1:54 μm wavelength.

[0084] Equivalents

[0085] While this invention has been particularly shown and describedwith references to preferred embodiments thereof, it will be understoodby those skilled in the art that various changes in form and details maybe made therein without departing from the scope of the inventionencompassed by the appended claims.

What is claimed is:
 1. A single crystal ceramic material for optical andoptoelectronic applications, comprising a single crystal spinel having ageneral formula aAD·bE₂D₃, wherein A is selected from the groupconsisting of Mg, Ca, Zn, Mn, Ba, Sr, Cd, Fe, and combinations thereof,E is selected from the group consisting Al, In, Cr, Sc, Lu, Fe, andcombinations thereof, and D is selected from the group consisting O, S,Se, and combinations thereof, wherein a ratio b:a>1:1 such that thespinel is rich in E₂D₃, and the single crystal spinel is formed by amelt process.
 2. The material of claim 1, wherein A is Mg, D is O, and Eis Al, such that the single crystal spinel has the formula aMgO.bAl₂O₃.3. The material of claim 1, wherein the single crystal spinel is grownfrom a melt provided in a crucible.
 4. The material of claim 1, whereinthe material has a lower mechanical stress and strain compared tostoichiometric spinel.
 5. The material of claim 1, wherein the materialconsists essentially of a single phase of said spinel, withsubstantially no secondary crystalline phases.
 6. The material of claim1, wherein b:a is not less than about 1.2:1.
 7. The material of claim 1,wherein b:a is not less than about 1.5:1.
 8. The material of claim 1,wherein b:a is not less than about 2.0:1.
 9. The material of claim 1,further comprising Co, wherein the ceramic material forms a saturableabsorber Q-switch.
 10. The material of claim 9, wherein the saturableabsorber Q-switch has a formula Mg_(1-x)Co_(x)Al_(y)O_(z) where x isgreater than 0 and less than about 1, y is greater than 2 and less thanabout 8, and z is between about 4 and about 13, said single crystalhaving tetrahedral and octahedral positions, and wherein most of themagnesium and cobalt occupy tetrahedral positions.
 11. A method offorming a monocrystalline spinel material, comprising: forming a melt;and growing a spinel single crystal from the melt, the single crystalspinel having a general formula aAD·bE₂D₃, wherein A is selected fromthe group consisting of Mg, Ca, Zn, Mn, Ba, Sr, Cd, Fe, and combinationsthereof, E is selected from the group consisting Al, In, Cr, Sc, Lu, Fe,and combinations thereof, and D is selected from the group consisting O,S, Se, and combinations thereof, wherein a ratio b:a>1:1 such that thespinel single crystal is rich in E₂D₃.
 12. The material of claim 11,wherein A is Mg, D is O, and E is Al, such that the single crystalspinel has the formula aMgO.bAl₂O₃.
 13. The material of claim 11,wherein b:a is not less than about 1.5:1.
 14. The method of claim 11,wherein the melt is provided in a crucible.
 15. The method of claim 11,wherein the single crystal is grown by contacting a seed crystal withthe melt.
 16. The method of claim 15, wherein the seed crystal and themelt are rotated with respect to each other during growing.
 17. Themethod of claim 16, wherein rotation is carried out at a rate within arange of about 2 to about 12 rpms.
 18. The method of claim 15, whereinthe seed crystal is withdrawn from the melt within a range of about 0.04inches/hour to about 0.1 inches/hour.
 19. The method of claim 11,wherein A is Mg, D is O, and E is Al, the spinel single crystal furtherincludes Co, and the spinel single crystal forms a saturable absorberQ-switch.
 20. The method of claim 19, wherein a molar ratio of Mg:Co:Alof the spinel is (1-x):x:y, where x is greater than 0 and less thanabout 1, and y is greater than 2 and less than about
 8. 21. The methodof claim 11, wherein the melt is heated to a temperature greater thanabout 2150° C.